The present invention relates to an optical frequency filter used to block or transmit an optical signal that is amplitude-modulated at a particular frequency, according to the modulation frequency and to an optical multiplexing circuit constructed by using the optical frequency filter.
An optical frequency filter, as shown in FIG. 1, is disclosed by the present inventor in the Japanese Laid-Open Patent Publication No. 57-62034 published on Apr. 14, 1982. In this filter an optical coupler 5 and an optical splitter 6 are connected with optical fibers 1 through 4.
In order to derive the frequency characteristic of the filter in FIG. 1, specific parameters will be defined as follows:
I.sub.i (t): intensity of light applied to the incident fiber 1, PA1 I.sub.o (t): intensity of light emerging from the emergent fiber 4, PA1 I.sub.m (t): intensity of light at the point E, PA1 G(s): transmission function of the filter expressed by Laplace transformation, PA1 .omega.: angular frequency of the modulation wave, PA1 t: time, PA1 T.sub.d : time required for light to transit through the entire fiber 3 (between the points B and D), EQU I.sub.o (S)=.epsilon..sub.1 .epsilon..sub.2 .epsilon..sub.3 e.spsp.-T.sup.d.spsp.s I.sub.i (s)+.epsilon..sub.2 .epsilon..sub.3 .epsilon..sub.5 .epsilon..sub.6 e.spsp.-T.sup.d.spsp.s I.sub.m (s), (3)
and EQU I.sub.m (s)=.epsilon..sub.1 .epsilon..sub.2 .epsilon..sub.4 e.spsp.-T.sup.d.spsp.s I.sub.i (s)+.epsilon..sub.2 .epsilon..sub.4 .epsilon..sub.5 .epsilon..sub.6 e.spsp.-T.sup.d.spsp.s I.sub.m (s).(4)
When rearranged, ##EQU1##
Therefore, ##EQU2##
Accordingly, the filter's frequency characteristic L is as indicated by the following expression (7): ##EQU3##
In expression (7), .beta..sub.1 through .beta..sub.6 and T.sub.d are constants. Accordingly, filter in FIG. 1 is disadvantageous in that the frequency characteristic thereof (or the quality factor Q of the filter) cannot be adjusted. Furthermore, the filter has a repetitive bandpass characteristic as shown in FIG. 2 (the characteristic curve indicacted by the dotted line being described later). Accordingly, the filter can pass a particular signal, but it cannot reject a specified signal.